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A223256 Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the numerator of the coefficient of x^k in the characteristic polynomial of the matrix realizing the transformation to Jacobi coordinates for a system of n particles on a line.

%I A223256 #12 Mar 20 2013 12:42:00
%S A223256 1,1,1,1,3,1,1,11,11,1,1,25,61,25,1,1,137,379,379,137,1,1,49,667,3023,
%T A223256 667,49,1,1,363,529,8731,8731,529,363,1,1,761,46847,62023,270961,
%U A223256 62023,46847,761,1,1,7129,51011,9161,28525,28525,9161,51011,7129,1
%N A223256 Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the numerator of the coefficient of x^k in the characteristic polynomial of the matrix realizing the transformation to Jacobi coordinates for a system of n particles on a line.
%C A223256 The matrix J(n) realizing the change of coordinates for n particles is
%C A223256 [1, -1, 0, 0, 0, ... 0],
%C A223256 [1/2, 1/2, -1, 0, ... 0],
%C A223256 [1/3, 1/3, 1/3, -1, 0 ... 0],
%C A223256 ...
%C A223256 [1/n, 1/n, 1/n, 1/n, ... 1/n]
%C A223256 Diagonals T(n,1)=T(n,n-1) are A001008, corresponding to the fact that the matrix J(n) above has trace equal to the n-th harmonic number.
%C A223256 See A223257 for denominators.
%H A223256 Wikipedia, <a href="http://en.wikipedia.org/wiki/Jacobi_coordinates">Jacobi coordinates</a>
%e A223256 Triangle begins:
%e A223256 1,
%e A223256 1, 1,
%e A223256 1, 3, 1,
%e A223256 1, 11, 11, 1,
%e A223256 1, 25, 61, 25, 1,
%e A223256 1, 137, 379, 379, 137, 1,
%e A223256 1, 49, 667, 3023, 667, 49, 1,
%e A223256 1, 363, 529, 8731, 8731, 529, 363, 1,
%e A223256 ...
%K A223256 easy,frac,nonn,tabl
%O A223256 0,5
%A A223256 _Alberto Tacchella_, Mar 18 2013